The company is scheduled to set a final price for its initial public offering late Wednesday and make its debut Thursday. The company may end the day with a market value of $25 billion, according to IG, which runs a gray market that lets investors bet on such outcomes.

A $25 billion market capitalization implies a share price of about $46 at the end of the first day. That compares with Twitter's current price range for the IPO of $23 to $25 a share, which implies a valuation of about $17 billion.

Twitter is the most anticipated technology IPO since Facebook's troubled market debut in May 2012. The microblogging service has become a media phenomenon, used by presidents, celebrities and kids alike. The company needs to make the platform easier to use, and big profits have yet to materialize, but Wall Street is still keen to get involved.

"Twitter is likely to become a core holding for many growth portfolios," says Brad Gastwirth, CEO of ABR Investment Strategy, an independent research firm focused on tech and health care.

Twitter raised its IPO price range Monday, and on Tuesday morning, the order book closed early, suggesting Goldman Sachs and the other banks underwriting the offering are seeing strong demand from investors.

He estimated the offering is at least 10 times oversubscribed, which means that investors have placed orders totaling at least 10 times the number of shares that will be sold.

"Even though Facebook's IPO was a disaster at first, this one is set up to perform a lot better," Wyman added.

Facebook priced its IPO at $38. The stock ended its first day just above that level, then slumped in the weeks following.

IG's gray market initially called for Facebook shares to end their first day of trading at about $30. However, on the last day before the market debut, exuberance got the better of IG clients as they bet that the stock would surge to $45 or even $48, Kelly says.

The opposite has happened with Twitter's IPO. About a month ago, IG clients were betting that Twitter would be valued at about $29 billion at the end of the first day of trading. That dropped to roughly $24 billion about a week ago, Kelly noted.